F(t)= 30000/1+20e^-1.5t

Describes the number of people, f(t), who have become ill with influenza t weeks after the initial outbreak in a town with 30,000 inhabitants.
a.) How many people became ill with flu when the epidemic began?
b.) How many people were ill by the end of the fourth week?

Surely you meant:

F(t)= 30000/(1+20e^-1.5t )

a) let t = -
F(0) = 30000/(1+20) = appr 1429

b) when t = 4
F(4) = 30000/(1 + 20e^-6)
= 28,583

check my "button-pushing" on the calculator

f(t) 30000

1+20e^-1.5(t)

To find the number of people who became ill with the flu when the epidemic began (a), we need to substitute t = 0 into the given equation.

a.) F(0) = 30000 / (1 + 20e^-1.5(0))
= 30000 / (1 + 20e^0)
= 30000 / (1 + 20)
= 30000 / 21
= 1428.57 approximately

Therefore, approximately 1429 people became ill with the flu when the epidemic began.

To find the number of people who were ill by the end of the fourth week (b), we need to substitute t = 4 into the given equation and solve.

b.) F(4) = 30000 / (1 + 20e^-1.5(4))
= 30000 / (1 + 20e^-6)
= 30000 / (1 + 20(1/e^6))
= 30000 / (1 + 20(1/403.43))
= 30000 / (1 + 0.04947)
= 30000 / (1.04947)
= 28594.13 approximately

Therefore, approximately 28594 people were ill by the end of the fourth week.